Two Symmetrohedra Which Each Feature Four Regular Enneagons

Posted on 6 January 2025 by RobertLovesPi

This symmetrohedron has the following faces: four regular enneagons, four equilateral triangles, and twelve isosceles triangles with vertex angles of 43.5686 degrees. Its net is shown below.

If this polyhedron is stellated once, the result is another symmetrohedron — one with four enneagonal faces, as well as twelve kites. The angles in the kites are 116.762, 99.8348, 43.5686, and 99.8348 degrees, and their side lengths are in a 1:2.2946 ratio.

Finally, here is a net for this kite-and-enneagon solid.

I used Stella 4d: Polyhedron Navigator to make everything you see here. If you’d like to try this software for yourself, a free trial download is available at http://www.software3d.com/Stella.php.

A 200-Faced Polyhedron Featuring Twenty Regular Enneagons

Posted on 6 October 2024 by RobertLovesPi

In addition to the regular enneagons, this polyhedron’s faces include sixty irregular hexagons, as well as sixty each of two different types of irregular pentagon. I made it using Stella 4d, which you can try for free at this website.

Two Polyhedra Which Both Feature Twenty Regular Enneagons

Posted on 4 October 2024 by RobertLovesPi

The first polyhedron shown here has 212 faces.

The next one has 120 faces, and all the non-enneagonal faces in it are convex pentagons — sixty each, of two types.

I made these polyhedra using Stella 4d, which you can try for free right here.

Two Symmetrohedra, Both of Which Feature Eight Regular Enneagons

Posted on 29 September 2024 by RobertLovesPi

The first of these, shown above, also includes six squares, 24 isosceles trapezoids, and twelve rectangles among its faces.

The second one, shown below, also includes among its faces six regular octagons, and twelve pairs of “bowtie” trapezoids.

I made both of these models using Stella 4d, which you can try for free here. The starting point for making them was the enneagonal-faced polyhedron found in this program’s built-in set of near-misses to the Johnson solids.